**Projective geometry is all geometry.**

The 228th day of the year; 228 is the number of ways, up to rotation and reflection, of dissecting a regular 11-gon into 9 triangles.

If the sum of its digits,12, is subtracted from 228, you get a cube, 228 - 12 = 216 = 6^3. If the product of its digits, 32, is subtracted, you get a square. 228 - 32 = 196 = 14^2

228 + 1, 822 + 1, and (228 + 822) + 1 are all primes. *Is there another such year day?*

228 in binary is written 11100100 notice that this is all four possible two digit binary combinations in descending order, 11, 10, 01, 00. (Just figured out that the equivalent in base three is a little over 10^{39})

228 is between twin primes

See More Math Facts for every Year Day, here

**1565 **The Grand Duchess Christina of Lorraine was born Aug. 16, 1565. Christina was the grand-daughter of Catherine d’ Medici, and she re-cemented her ties to the family in 1589, when she married Ferdinando I de’ Medici of Florence in a lavish wedding. Christina hired Galileo Galilei, then at Padua, to tutor her eldest son, Cosimo II, and when Christina’s husband died in 1609, Cosimo succeeded him as Grand Duke of Tuscany, and Christina stayed on at the court. Galileo gave Cosimo the telescope with which he discovered the four moons of Jupiter in 1610, naming them the “Medicean stars” in his honor. After Galileo joined the Medici court, he became well acquainted with the Duchess (who was actually a year younger than Galileo), and on several occasions she asked Galileo how the Copernican idea of a moving earth could be compatible with those passages of Scripture that discuss a fixed earth and a moving sun. In response, Galileo wrote, in 1615, what is usually called the Letter to the Grand Duchess Christina, in which he suggested that the language of the Bible was written to “accommodate” the understanding of the ordinary person and was not intended to be taken literally. He further argued that the Bible was intended to indicate the road to salvation, and was not meant to provide instruction in natural philosophy.

This letter circulated in manuscript and was brought to the attention of Cardinal Bellarmine, the principal theological advisor to the Pope. Bellarmine ruled that accomodationism was acceptable when one could prove that the Bible had to be read some way other than literally, but first you needed proof, and Galileo had no proof that the earth moved. Therefore scriptural passages suggesting a fixed Earth should be read literally. A committee then pronounced in 1616 that Copernicanism was heretical, and Copernicus’ book On the Revolutions (1543) was, for the first time, placed on the Index of Prohibited Books. Galileo’s trial was still 16 years away, but the stage had now been set, thanks to the Letter to Christina. *Linda Hall Org

**1811 ** “Having to conduct my grandson through his course of mathematics, I have resumed the study

with great avidity. It was ever my favorite one. We have no theories there, no uncertainties

remain on the mind; all is demonstration and satisfaction.” So wrote Thomas Jefferson (1743–

1826) to Benjamin Rush. Taken from The Writings of Thomas Jefferson, edited by A. A. Lipscomb, vol. 13 (1903), p. 75, as quoted from Cajori, Mathematics in Liberal Education, p. 109,

which is a collection of interesting quotations on the value of mathematics.

**1825 **A royal decree granted Neils Henrik Abel, then 23, sufficient funds for a year’s travel in France and Germany. *VFR

In 1815 Niels entered the cathedral school in Oslo, where his mathematical talent was recognized in 1817 with the arrival of a new mathematics teacher, Bernt Michael Holmboe, who introduced him to the classics in mathematical literature and proposed original problems for him to solve.

Abel’s father died in 1820, leaving the family in straitened circumstances, but Holmboe contributed and raised funds that enabled Abel to enter the University of Christiania (Oslo) in 1821. Abel obtained a preliminary degree from the university in 1822 and continued his studies independently with further subsidies obtained by Holmboe.

Abel’s first papers, published in 1823, were on functional equations and integrals; he was the first person to formulate and solve an integral equation. His friends urged the Norwegian government to grant him a fellowship for study in Germany and France. In 1824, while waiting for a royal decree to be issued, he published at his own expense his proof of the impossibility of solving algebraically the general equation of the fifth degree, which he hoped would bring him recognition. He sent the pamphlet to Gauss, who dismissed it, failing to recognize that the famous problem had indeed been settled.

In 1858, Queen Victoria sent the first official telegraph message across the Atlantic Ocean from London to the US. (Test messages had been exchanged for 10 days). Her message to President Buchanan, in Washington DC, began transmission at 10:50am and was completed at 4:30am the next day, taking nearly 18-hrs to reach Newfoundland. With 99 words, consisting of 509 letters, it averaged about 2-min per letter. The message was forwarded across Newfoundland by an overhead wire supported on poles; across Cabot Strait by submarine cable to Aspy Bay (Dingwall), Cape Breton; and by an overhead wire across eastern Canada and Maine, via Boston to New York. This earliest Transatlantic cable went dead within a month.

**1878** Hermite writes to Sylvester at Johns Hopkins concerned about his accepting a Math Chair in America to questioned the ability of the American people to contribute to research-level mathematics. Only three years later he would be reading the paper of Fabian Franklin, a young assistant mathematics instructor at Johns Hopkins, before the French Academy. The paper was on a short, purely graphic, proof of Euler's theorem on pentagonal numbers. *Karen Hunger Parshall, David E. Rowe; The Emergence of the American Mathematical Research Community, 1876-1900 Franklin would later wed Christine Ladd-Franklin (1882 ir 1884?).

1890 The US Census Bureau announces the U.S. population of 62,622,250, determined for the first time by using an automated method, the Hollerith Census Machine. The Hollerith machine sorted returns by completing an electrical circuit wherever a hole existed in a punch card and could process almost 10 times the number of census data than a human clerk.

Census workers used the Punch Pantograph to enter data. Hollerith formed the Tabulating Machine Company in 1896. This company merged with two others in 1924 to become the International Business Machines company or IBM. Hollerith died November 17, 1929.

**In 1898**, the loop-de-loop Roller Coaster was patented by Edwin Prescott.*TIS The vertical loop is not a recent roller coaster innovation. Its origins can be traced back to the 1850s when centrifugal railways were built in France and Great Britain. In 1901 Prescott built the Loop-the-Loop at Coney Island. This ride used the modern teardrop-shaped loop and a steel structure, however more people wanted to watch the attraction, rather than ride. No more looping roller coasters were built until 1976 when Revolution opened at Six Flags Magic Mountain.*Wik

*Smithsonian |

**1941** When Herbert Robbins saw the proof sheet of the title page of What is Mathematics? with only the name Richard Courant on it, his first reaction was “My god, the man’s a crook.” Realizing that a quiet meeting on their co-authorship of the book would be impossible, Robbins wrote Courant on this date that, while the custom might be different in Europe, in this country the junior author did receive credit. Courant backed down, and so today we know this lovely book as one by Courant and Robbins.

**1966 Stephen Smale**, University of California, Berkeley, received the Fields Medal at the International Congress of Mathematicians in Moscow for his work on dynamical systems. Ten days later on the steps of Moscow University he will make a speech condemning American

military activity in Vietnam and Soviet military involvement in Hungary. *VFR

**1983** Poland issued a stamp celebrating the 50th anniversary of the Enigma Decoding Machine. VFR

**1744 Pierre (-François-André) Méchain **(16 Aug 1744; 20 Sep 1804). a French astronomer and hydrographer at the naval map archives in Paris recruited by Jean Delambre. He was a mathematical progidy. In 1790, they were chosen by the National Assembly to establish a decimal system of measurement based on the meter. Since this was defined to be one ten-millionth of the distance between the Earth's pole and the equator, Mechain led a survey of the meridian arc from Dunkirk, France, to Barcelona, Spain. Through his astronomical observations, Mechain discovered 11 comets and provided 26 additions to Messier's catalog. He calculated the orbits of the two comets he found in 1781. Mechain died of yellow fever while making further surveys for the meridian measurement. *TIS

Méchain discovered a number of deep-sky nebulous objects, including M101 (the Pinwheel Galaxy; shown), M87 (the Owl Nebula), and M104 (the Sombrero Galaxy).

*Wik |

**1821 Arthur Cayley**, (16 August 1821 – 26 January 1895) English mathematician who played a leading role in founding the modern British school of pure mathematics. He trained first as a lawyer, and from 1849, spent 14 years at the bar, during which time he maintained an interest in mathematics and published about 250 mathematical papers. In 1863, Cayley followed his passion and commenced a new career as professor of Pure Mathematics at Cambridge and during his tenure published 900 papers and notes covering nearly every aspect of modern mathematics. The legacy of his work in n-dimensional geometry was later applied in physics to the study of the space-time continuum. His work on matrices served as a foundation for quantum mechanics developed by Werner Heisenberg in 1925. *TIS

**1836 Marc-Antoine Parseval des Chênes** (April 27, 1755 – August 16, 1836) was a French mathematician, most famous for what is now known as Parseval's theorem, which presaged the unitarity of the Fourier transform.

He was nominated to the French Academy of Sciences five times, from 1796 to 1828, but was never elected. His only mathematical publications were, apparently, five papers, published in 1806 as *Mémoires présentés à l'Institut des Sciences, Lettres et Arts, par divers savants, et lus dans ses assemblées. Sciences mathématiques et physiques. (Savants étrangers.)* This combined the following earlier monographs:

- "Mémoire sur la résolution des équations aux différences partielles linéaires du second ordre," (May 5, 1798).
- "Mémoire sur les séries et sur l'intégration complète d'une équation aux différences partielles linéaires du second ordre, à coefficients constants," (April 5, 1799).
- "Intégration générale et complète des équations de la propagation du son, l'air étant considéré avec ses trois dimensions," (July 5, 1801).
- "Intégration générale et complète de deux équations importantes dans la mécanique des fluides," (August 16, 1803).
- "Méthode générale pour sommer, par le moyen des intégrales définies, la suite donnée par le théorème de M. Lagrange, au moyen de laquelle il trouve une valeur qui satisfait à une équation algébrique ou transcendante," (May 7, 1804).

It was in the second, 1799, memoir in which he stated, but did not prove (claiming it to be self-evident), the theorem that now bears his name. He further expanded upon it in his 1801 memoir, and used it to solve various differential equations. The theorem was first printed in 1800 as a part (p. 377) of *Traité des différences et des séries* by Lacroix.

*Wik

**1837 Joseph-Marie de Tilly**,(16 Aug 1837 in Ypres, Belgium - 4 Aug 1906 in Munich, Germany) Belgian mathematician, born. In 1899 he was dismissed from his teaching post at the Ecole Militaire for unduly emphasizing the scientific education of future officers and using the notions of the inﬁnitely small and the differential. *VFR

**1845 Gabriel Lippman** (16 Aug 1845; 13 Jul 1921).French physicist, born Hollerich, Luxembourg, who received the Nobel Prize for Physics in 1908 for producing the first colour photographic plate. Lippmann was a giant of his day in classical physics research, especially in optics and electricity. He worked in Berlin with the famed Hermann von Helmholtz before settling in Paris to head (in 1886) the Sorbonne's Laboratories of Physical Research until his death. His inventions include an instrument for precisely measuring minute differences in electrical power and the "coleostat" for steady, long-exposure sky photography.*TIS\

**1884 Hugo Gernsback** (August 16, 1884 – August 19, 1967), born Hugo Gernsbacher, was a Luxembourgish-American inventor, writer, editor, and magazine publisher, best known for publications including the first science fiction magazine. His contributions to the genre as publisher were so significant that, along with the novelists H. G. Wells and Jules Verne, he is sometimes called "The Father of Science Fiction". In his honor, annual awards presented at the World Science Fiction Convention are named the "Hugos" *Wik

Gernsback's second novel, Baron Münchausen's Scientific Adventures, was serialized in Amazing in 1928, with the opening installment taking the February cover

**1904 Wendell Meredith Stanley** (16 August 1904 – 15 June 1971) was an American biochemist, virologist and Nobel laureate. Stanley was born in Ridgeville, Indiana, and earned a BS in Chemistry at Earlham College in Richmond, Indiana. He then studied at the University of Illinois, gaining an MS in science in 1927 followed by a Ph.D. in chemistry two years later. His later accomplishments include writing the book "Chemistry: A Beautiful Thing" and achieving his high stature as a Pulitzer Prize nominee.

Stanley was awarded the Nobel Prize in Chemistry for 1946. His other notable awards included the Rosenburger Medal, Alder Prize, Scott Award, and the AMA Scientific Achievement Award. He was also awarded honorary degrees by many universities both American and foreign, including Harvard, Yale, Princeton and the University of Paris. Most of the conclusions Stanley had presented in his Nobel-winning research were soon shown to be incorrect (in particular, that the crystals of mosaic virus he had isolated were pure protein, and assembled by autocatalysis)

Stanley married Marian Staples (1905-1984) in 1929 and had three daughters (Marjorie, Dorothy and Janet), and a son, (Wendell M. Junior). Stanley Hall at UC Berkeley (now Stanley Biosciences and Bioengineering Facility) and Stanley Hall at Earlham College are named in his honor. *Win

**1905 Marian Adam Rejewski** (16 August 1905 – 13 February 1980) was a Polish mathematician and cryptologist who in 1932 solved the plugboard-equipped Enigma machine, the main cipher device used by Germany. The success of Rejewski and his colleagues Jerzy Różycki and Henryk Zygalski jump-started British reading of Enigma in World War II; the intelligence so gained, code-named "Ultra", contributed, perhaps decisively, to the defeat of Nazi Germany.

While studying mathematics at Poznań University, Rejewski had attended a secret cryptology course conducted by the Polish General Staff's Biuro Szyfrów (Cipher Bureau), which he joined full-time in 1932. The Bureau had achieved little success reading Enigma and in late 1932 set Rejewski to work on the problem. After only a few weeks, he deduced the secret internal wiring of the Enigma. Rejewski and his two mathematician colleagues then developed an assortment of techniques for the regular decryption of Enigma messages. Rejewski's contributions included devising the cryptologic "card catalog," derived using his "cyclometer," and the "cryptologic bomb."

Five weeks before the German invasion of Poland in 1939, Rejewski and his colleagues presented their results on Enigma decryption to French and British intelligence representatives. Shortly after the outbreak of war, the Polish cryptologists were evacuated to France, where they continued their work in collaboration with the British and French. They were again compelled to evacuate after the fall of France in June 1940, but within months returned to work undercover in Vichy France. After the country was fully occupied by Germany in November 1942, Rejewski and fellow mathematician Henryk Zygalski fled, via Spain, Portugal and Gibraltar, to Britain. There they worked at a Polish Army unit, solving low-level German ciphers. In 1946 Rejewski returned to his family in Poland and worked as an accountant, remaining silent about his cryptologic work until 1967. *Wik

**1907 Dura Kurepa** (16 Aug 1907, 2 Nov 1993)The topics which Kurepa investigated are very varied but lie mostly within topology, set theory and number theory. He published over 200 papers but this number rises to over 700 items if we include books, articles and reviews. He was fascinated by the continuum hypothesis and the axiom of choice. Perhaps best known is his work on trees and partitions, especially Aronszajn and Suslin trees. His book The Theory of Sets written in Serbo-Croatian and published in 1951 illustrates his interests in that particular area. After introducing the fundamental concepts and elementary operations in Chapter 1, he looks at cardinal numbers in the second chapter, then partially ordered sets and ordinal numbers in the third. Chapter 4 is on topological and metric spaces, with the fifth and final chapter on limiting processes in analysis, measure theory, Borel and Souslin sets.

In number theory he made many contributions, but perhaps his most famous is his open problem on the left factorial function. In 1971 he published his definition of !n, the left factorial function, defined by

!n = 0! + 1! + 2! + 3! + ... + (n-1)!.

Kurepa conjectured that the greatest common divisor of !n and n! was 2 for all n > 1. There are many equivalent forms of the conjecture, but one of the most natural was given by Kurepa in the same 1971 paper, namely that !n is not divisible by n for any n > 2. If the left factorial conjecture is false we certainly know that it will fail for n > 1000000.*SAU

The same left factorial notation is more commonly used for the subfactorial used in derangements. Many mathematicians simply use "factorial sum" for Kurepa's !n. It is interesting that no one seems to have picked up on the use of an inverted exclamation point as suggested by G. Chrystal in his "Algebra, an Elementary Textbook for the Higher Classes of Secondary Schools and for Colleges", (1889 (pg 25))

**1920 Richard Ernest Bellman **(August 26, 1920 – March 19, 1984) was an American applied mathematician, celebrated for his invention of dynamic programming in 1953, and important contributions in other fields of mathematics. A Bellman equation, also known as a dynamic programming equation, is a necessary condition for optimality associated with the mathematical optimization method known as dynamic programming. Almost any problem which can be solved using optimal control theory can also be solved by analyzing the appropriate Bellman equation. The Bellman equation was first applied to engineering control theory and to other topics in applied mathematics, and subsequently became an important tool in economic theory. The "Curse of dimensionality", is a term coined by Bellman to describe the problem caused by the exponential increase in volume associated with adding extra dimensions to a (mathematical) space.*Wik

**1958 Anne Geneviève L'Huillier** ( born 16 August 1958, ) is a French physicist, and professor of atomic physics at Lund University in Sweden.

She leads an attosecond (10^-18) physics group which studies the movements of electrons in real time, which is used to understand the chemical reactions on the atomic level. Her experimental and theoretical research are credited with laying the foundation for the field of attochemistry. In 2003 she and her group beat the world record for the shortest laser pulse, of 170 attoseconds.

L'Huillier became a member of the Royal Swedish Academy of Sciences in 2004. She has received various physics awards including the Wolf Prize in Physics in 2022 and the Nobel Prize in Physics in 2023.

**1705 Jakob Bernoulli **. (27 December 1654 – 16 August 1705) He was so fascinated with the way the logarithmic spiral reproduces itself in its involute, its evolute, and its caustics of reﬂection and refraction, that he requested it be engraved on his tombstone, together with the inscription Eadem mutata resurgo (Though changed, I will arise the same). *VFR (the spiral on his tombstone is not logarithmic, but Archimedian... perhaps he is spinning in his grave even yet.)

He was one of the first to fully utilize differential calculus and introduced the term "integral" in integral calculus. Jacob Bernoulli's first important contributions were a pamphlet on the parallels of logic and algebra (1685), work on probability in 1685 and geometry in 1687. His geometry result gave a construction to divide any

triangle into four equal parts with two perpendicular lines.(*a nice exercise to try*)

----A short digression about this quadrisection construction -----------

He gave a general algebraic solution which required finding a root of a polynomial of degree 8 and worked this out numerically for one scalene triangle.The question of whether Bernoulli’s polynomial equation of degree 8 has the needed root in all cases is not answered completely.

Leonhard Euler wrote a 22 page paper in 1779 in which he gives a complete solution using trigonometry.

Euler states his solution in a theorem which we paraphrase.

Theorem 1. (Euler 1779) Given a scalene triangle ∆ABC with AB the side of middle length, there is a quadrisection XP and Y Q intersecting in a point O in the interior of the triangle so that X and Y lie on side AB and triangle XOY is one of the 4 areas of the quadrisection. The other areas of the quadrisection are quadrangles. Euler does not claim that the triangular portion of a quadrisection must lie on the side of middle length. Also, he does not appear to discuss whether there is more than one quadrisection of a triangle, except to note that an equilateral triangle has 3 quadrisections. In fact, we will see there are lots of triangles with quadrisections where the triangular portion lies on the shortest side, but no triangles having a quadrisection with the triangular portion on the longest side.

Revisiting the quadrisection problem of Jacob Bernoulli. Carl Eberhart

------------------------End Digression------------------

By 1689 he had published important work on infinite series and published his law of large numbers in probability theory. He published five treatises on infinite series (1682 - 1704). He was the first of the Bernoulli family of mathematicians. *TIS

Jacob Bernoulli’s Ars Conjectandi from 1713 is the first major book on the theory of probability and statistics. It is because of its 300 years anniversary that 2013 was named the international year of Statistics. The exhibited copy is in fact a first edition! It is showing the proof of the law of large numbers, one of the results for which it is famous. * University of Copenhagen Dept of Math Sciences

**1899 Robert Wilhelm Eberhard Bunsen **(30 March 1811[?) – 16 August 1899) was a German chemist. He investigated emission spectra of heated elements, and discovered caesium (in 1860) and rubidium (in 1861) with the physicist Gustav Kirchhoff. The Bunsen–Kirchhoff Award for spectroscopy is named after Bunsen and Kirchhoff.

Bunsen also developed several gas-analytical methods, was a pioneer in photochemistry, and did early work in the field of organic arsenic chemistry. With his laboratory assistant Peter Desaga, he developed the Bunsen burner, an improvement on the laboratory burners then in use. *Wik

His Bunsen burner was created for use in flame tests of various metals and salts because its nonluminous flame did not interfere with the colored flame given off by the test material.*TiS

**1920 Sir Joseph Norman Lockyer** (17 May 1836, 16 Aug 1920) British astronomer who in 1868 discovered and named the element helium that he found in the Sun's atmosphere before it had been detected on Earth. He also applied the name chromosphere for the sun's outer layer. Lockyer discovered, together with Pierre J. Janssen, the prominences (red flames) that surround the solar disk. He was also interested in the classification of stellar spectra and developed the meteoric hypothesis of stellar evolution. His works include the books Contributions to Solar Physics (1873), The Sun's Place in Nature (1897) and Inorganic Evolution (1900). *TIS

A solar prominence (also known as a filament when viewed against the solar disk) is a large, bright feature extending outward from the Sun's surface. Prominences are anchored to the Sun's surface in the photosphere, and extend outwards into the Sun's hot outer atmosphere, called the corona.

**1995 Thomas Brooke Benjamin,** FRS (15 April 1929 – 16 August 1995) was an English mathematical physicist and mathematician, best known for his work in mathematical analysis and fluid mechanics, especially in applications of nonlinear differential equations. *Wik

**2013 David Rees FRS** (29 May 1918 – 16 August 2013) was a British professor of pure mathematics at the University of Exeter, having been head of the Mathematics / Mathematical Sciences Department at Exeter from 1958 to 1983. During the Second World War, Rees was active on Enigma research in Hut 6 at Bletchley Park.

Rees won a scholarship to Sidney Sussex College, Cambridge, supervised by Gordon Welchman and graduating in summer 1939. On completion of his education, he initially worked on semigroup theory; the Rees factor semigroup is named after him. He also characterised completely simple and completely 0-simple semigroups, in what is nowadays known as Rees's theorem. The matrix-based semigroups used in this characterisation are called Rees matrix semigroups.

Later in 1939, Welchman drafted Rees into Hut 6, Bletchley Park, for the war effort. He was credited with the first decode using the Herivel tip. He was subsequently seconded to the Enigma Research Section, where the Abwehr Enigma was broken, and later to the Newmanry, where the Colossus computer was built.

After the war, Rees was appointed an assistant lecturer at Manchester University in 1945 and a full lecturer at University of Cambridge in 1948. In 1949, he was a Fellow of Downing College.

At the behest of Douglas Northcott he switched his research focus to commutative algebra.[10] In 1954, in a joint paper with Northcott, Rees introduced the Northcott–Rees theory of reductions and integral closures, which has subsequently been influential in commutative algebra. In 1956 he introduced the Rees decomposition of a commutative algebra.

In 1958, Rees and his family moved to Exeter, where he had been appointed to the Chair of Pure Mathematics. In 1959, he was awarded a DSc by the University of Cambridge.

According to Craig Steven Wright, Rees was the third part of the Satoshi team that created Bitcoin.*Wik

Credits :

*CHM=Computer History Museum

*FFF=Kane, Famous First Facts

*NSEC= NASA Solar Eclipse Calendar

*RMAT= The Renaissance Mathematicus, Thony Christie

*SAU=St Andrews Univ. Math History

*TIA = Today in Astronomy

*TIS= Today in Science History

*VFR = V Frederick Rickey, USMA

*Wik = Wikipedia

*WM = Women of Mathematics, Grinstein & Campbell

## No comments:

Post a Comment